iii. Finally, execute a counterclockwise rotation $L_\theta$. Determine $A_3$ such that $L_\theta(\underline{x}) = A_3\underline{x}$. Calculate $A = A_3A_2A_1$. (The result should match the answer given in part (a).)

Figure 1: $Col(A)$ denotes the column space of $A$.

Figure 2: Project $\underline{x}$ onto the line $l$ that forms an angle $\theta$ with the $X$-axis.

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